1. 1 Towards streaming hyperspectral endmember extraction Dževdet Burazerović, Rob Heylen, Paul Scheunders IBBT-Visionlab, University of Antwerp, Belgium IGARSS 2011 July 24-29, Vancouver, Canada

2. 2 Outline Prior art and motivation -LMM, N-findr The proposed algorithm -Distance-based simplex formulation -Streaming endmember estimation Experiments and results Conclusions

3. 3 Linear mixture model An observed spectrum x is a (constrained) linear sum of p endmember (EM) spectra e i : Then, EMs = vertices of the largest ( p -1 )-dim. simplex enclosing (most of) the x : e1e1 e3e3 e2e2 e4e4 x

4. 4 N-findr Estimates the largest simplex via repetitive vertex replacements ─ “single replacement” (SR) vs. “best replacement” (BR) ─ “single iteration” (SI) vs. “full iteration” (FI) Random initialNo replacementReplacement 1 2 3 1 2

5. 5 Motivation Finding the largest simplex is not sufficient/necessary (in real data, un-supervised scenarios) Worthwhile to seek efficient implementations (*) S. Dowler, M. Andrews: “On the convergence of N-findr …”, IEEE GRS Letters, 2011 (*)

6. 6 The proposed algorithm Extract EMs in 1-pass, streaming (online) fashion 1.Reformulate the simplex-vol. measurement to avoid dim. red. 2.Grow a suitable initial simplex for a given # of EMs 3.Maximize this simplex by subsequent replacements (N-findr) normally, n > p image epep

7. 7 Distance-based simplex formulation Via Cayley-Menger determinant, Schur complement V3V3 e1e1 e2e2 e3e3 e4e4

8. 8 Growing the initial simplex 0 1 V3V3 h h ~ V 4 /V 3 Use empirical CDFs to set thresh. for the simplex-vol. increment E.g., add x k as p-th EM, if F P (V k /V P-1 )≥0.5

9. 9 Comparison setup Acknowledge the variability of both algorithms ─ Streaming:threshold function for growing the initial simplex ─ N-findr:random selection of the initial simplex (EMs) Compare results (EMs) from multiple runs Use cluster validation to determine consistent EMs M– EMs K– runs M x K– data points

10. 10 Cluster validation i = 9 (13 spectra) i = 7 Results with N-findr, on Cuprite

11. 11 Comparison results Ground truth: P EM-cluster centroids from ~40 runs of N-findr Test data: P EMs from a single streaming pass Classification: N-Neighbor + visual comparison of the spectra Accuracy:13/18 (72.2%) on Cuprite, 4/7 (71.4%) on M.F. Cuprite, P=18 (350 x 350 x 188) Moffet Field, P=7 (335 x 370 x 56)

12. 12 Conclusions The use of dist.-based simplex formulation enables a new paradigm of EM-extraction: ─ A streaming (online) implementation based on N-findr ─ Avoiding the need to pre-load the entire image into memory Tested on diverse data, finds most of the EMs that are found by repetition of the reference methods (N-findr) Possible extension to other strategies for streaming-based simplex estimation and measurement